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We show that two popular selective inference procedures, namely data carving (Fithian et al., 2017) and selection with a randomized response (Tian et al., 2018b), when combined with the polyhedral method (Lee et al., 2016), result in confidence intervals whose length is bounded.
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Can one estimate the conditional distribution of post-model-selection estimators?
Leeb, H. and Pötscher, B. M. (2006) · 2006
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Testing statistical hypotheses
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Can one estimate the unconditional distribution of post-model-selection estimators?
Leeb, H. and Pötscher, B. M. (2008) · 2008
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Post-selection inference via algorithmic stability
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Valid post-selection inference
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Exact post-selection inference, with application to the lasso
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Selective sampling after solving a convex problem
Tian, X., Panograhi, S. a. M. J., Bi, N., and Taylor, J. (2016) · 2016
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Exact post-selection inference for sequential regression procedures
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Reid, S., Taylor, J., and Tibshirani, R. (2018) · 2018
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Post-selection inference for l 1 l_{1} -penalized likelihood models
Taylor, J. and Tibshirani, R. (2018) · 2018
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Selective inference with unknown variance via the square-root lasso
Tian, X., Loftus, J. R., and Taylor, J. E. (2018) · 2018
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Selective inference with a randomized response
Tian, X. and Taylor, J. (2018) · 2018
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Valid confidence intervals for post-model-selection predictors
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Tibshirani, R. J., Taylor, J., Lockhart, R., and Tibshirani, R. (2016) · 2016
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Optimal inference after model selection
Fithian, W., Sun, D. L., and Taylor, J. (2017) · 2017
Cited alongside, same era.
Post-selection point and interval estimation of signal sizes in gaussian samples
Reid, S., Taylor, J., and Tibshirani, R. (2017) · 2017
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Asymptotics of selective inference
Tian, X. and Taylor, J. (2017) · 2017
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Unifying approach to selective inference with applications to cross-validation
Markovic, J., Xia, L., and Taylor, J. (2018) · 2018
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A model free perspective for linear regression: Uniform-in-model bounds for post selection inference
Kuchibhotla, A. K., Brown, L. D., Buja, A., George, E. I., and Zhao, L. (2018a)
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Valid post-selection inference in assumption-lean linear regression
Kuchibhotla, A. K., Brown, L. D., Buja, A., George, E. I., and Zhao, L. (2018b)
Cited in the paper.
Bachoc, F., Leeb, H., and Pötscher, B. M. (2019) · 2019
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Post-selection estimation and testing following aggregate association tests
Heller, R., Meir, A., and Chatterjee, N. (2019) · 2019
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Uniformly valid confidence intervals post-model-selection
Bachoc, F., Preinerstorfer, D., and Steinberger, L. (2020) · 2020
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On the length of post-model-selection confidence intervals conditional on polyhedral constraints
Kivaranovic, D. and Leeb, H. (2021) · 2021
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